1\name{moranI}
2
3\alias{moranI}
4
5\title{Moran's I Autocorrelation Statistic}
6
7
8\description{
9Moran's I statistic measures autocorrelation between areas within
10a region. It is similar to the correlation coefficient:
11
12\deqn{
13I=\frac{n\sum_i\sum_j W_{ij}(Z_i-\overline{Z})(Z_j-\overline{Z})}{2(\sum_i\sum_jW_{ij})\sum_k (Z_k-\overline{Z})^2}
14}{
15I= n * [sum_i ( sum_j W_ij(Z_i-mean(Z))*(Z_j-mean(Z))]/[2 * (sum_i sum_j W_ij) * sum_k (Z_k-mean(Z))^2]
16}
17
18\eqn{W}{W} is a squared matrix which represents the relationship between each
19pair of regions. An usual approach is set \eqn{w_{ij}}{w_ij} to 1 if regions
20\eqn{i}{i} and \eqn{j}{j} have a common boundary and 0 otherwise, or it may
21represent the inverse distance between the centroids of these two regions.
22
23High values of this statistic may indicate the presence of groups of zones
24where values are unusually high. On the other hand, low values
25of the Moran's statistic will indicate no correlation between neighbouring
26areas, which may lead to indipendance in the observations.
27
28
29\emph{moranI.stat} is the function to calculate the value of the statistic for
30residuals or SMRs of the data.
31
32\emph{moranI.boot} is used when performing a non-parametric bootstrap.
33
34\emph{moranI.pboot} is used when performing a parametric bootstrap.
35}
36
37
38\seealso{
39DCluster, moranI.stat, moranI.boot, moranI.pboot
40}
41
42\references{
43Moran, P. A. P. (1948). The interpretation os statistical maps. Journal of the Royal Statistical Society, Series B 10, 243-251.
44}
45
46\keyword{spatial}
47